1. Field of the Invention
This patent specification relates to sonic logging and borehole seismic data using downhole tools. More particularly, this patent specification relates to systems and methods for combining sonic logging data with borehole seismic data including a calculation of elastic constants describing anisotropy.
2. Background of the Invention
Elastic properties are useful for many applications in subsurface engineering. For example, knowledge of the elastic properties which describe the subsurface seismic velocities is required for accurate imaging by seismic methods. Of particular interest is the elastic anisotropy of a rock, that is, the variation of its mechanical strength with direction. Elastic properties can be derived from sonic logs where high frequency seismic sources are deployed in the well and the resulting waves recorded using receivers that are also deployed in the well. Such sonic logs measure high spatial resolution estimates of the elastic properties around the well bore. Elastic estimates of the region around the well can also be derived from walkaway Vertical Seismic Profiles (VSP).
It is known that the elastic properties of a solid are fully described using 21 elastic constants. However, in many situations the elastic response can be well described using fewer parameters. For example in the case of a solid whose properties are invariant with the direction in which they are measured only two elastic constants are required. Materials with this behavior are called isotropic. Materials whose properties change with direction are called anisotropic with various subsets describing certain types of directional symmetries. A common form of anisotropy that is often observed in the earth is that of Transverse Isotropy where properties change only with respect to a single direction. An example can be constructed from the stacking of thin isotropic layers. The properties of the stack will change only with respect to the layer normal but is otherwise isotropic with respect to the direction transverse to the normal direction. Such Transverse Isotropy (TI) can be described using 5 elastic constants or equivalent parameterizations such as those described by Thomsen (1986) which have been widely adopted in the seismic industry. The Thomsen parameters are; Vp0, Vs0 which are the Compressional and Shear wave velocities along the symmetry axis, and ε, δ and γ which are dimensionless parameters describing the directional variations. Thomsen's ε describes the difference in the compressional-wave velocities measured along the symmetry axis and at right angles to it. Similarly, γ measures the difference between the shear-wave velocity measured along the symmetry axis and at right angles to it. The third Thomsen parameter, δ, is less easily described as the resulting velocity behavior depends on both ε and δ.
Modern sonic tools such as DSI™ and Sonic Scanner™ from Schlumberger are able to measure four wave types from which two elastic constants can be computed (C44 and C66) and two other elastic parameters (mC33, N) that are a combination of the other elastic constants (See, e.g., Norris, A. N. and Sinha, B. K., 1993, Weak elastic anisotropy and the tube wave, Geophysics 58, 1091-1098, incorporated by reference herein and referred to herein as “Norris and Sinha (1993)”). To resolve all the Thomsen parameters from these four parameters the ANNIE model can be used (See, e.g. Schoenberg, M., Muir, F., and Sayers, C. M., 1996, Introducing ANNIE: A simple three-parameter anisotropic velocity model for shales: Journal of Seismic Exploration, 5, 35-49, incorporated by reference herein and referred to herein as “Schoenberg, Muir, and Sayers (1996)”). The ANNIE model can sometimes be a good approximation for shales and implies that Thomsen's delta is zero. However, such an approximation may not always be appropriate, as is demonstrated in FIGS. 1a-d are a series of plots showing reported measurements of the Thomsen anisotropic parameters of ε and δ, as is known in the art. In particular Thomsen anisotropic parameters of ε and δ for Kimmeridge Shale is shown in FIGS. 1a and 1b, and for Bakken Shale in FIGS. 1c and 1d. It can be seen in the plots of FIGS. 1b and 1d that Thomsen's δ parameter is generally not equal to 0 as required by the ANNIE model (line 112 in FIG. 1b and line 116 in FIG. 1d). This suggests that the ANNIE model may not always be a good approximation. However, in FIGS. 1a and 1c we also observe that the Thomsen's anisotropy parameters of ε and γ are strongly correlated as has been observed by many authors (see, e.g. Wang, Z., 2002, Seismic anisotropy in sedimentary rocks, part 2: Laboratory data; Geophysics 67 (5) 1423-1440 (referred to herein as “Wang (2002)”, Sondergeld, C. H., Chandra, S. R., Margesson, R. W., & Whidden, K. J., 2000, Ultrasonic measurement of anisotropy on the Kimmeridge Shale, SEG Annual Meeting Expanded Abstracts; and Tsuneyama, F., and Mavko, G., 2005, Velocity anisotropy estimation for brine-saturated sandstone and shale, The Leading Edge, 882-888, all of which are incorporated by reference herein). Furthermore this degree of correlation, shown as line 110 in FIG. 1a, and line 114 in FIG. 1c, is formation dependent, in the Kimmeridge shale it is approximately 0.75 and for the Bakken Shale it is approximately 0.97.
The extraction of anisotropy parameters from walkaway VSP measurements can be considered. In general, there are two methods for deriving the elastic constants around the downhole receiver array. The first method is that of the slowness technique, (see, e.g. Miller, D. E., Leaney, S., and Borland, W. H., 1994, An in-situ estimation of anisotropic elastic moduli for a submarine shale, Journal of Geophysical Research, 99, 21659-21665, incorporated by reference herein), which requires a near horizontally layered overburden. The second method is that of slowness-polarization (see, e.g. de Parscau, J., 1991, P- and SV-wave transversely isotropic phase velocity analysis from VSP data. Geophysical Journal International 107, 629-638, incorporated by reference herein), which does not require structural simplicity in the overburden, as does the slowness method. In general these methods extract only four of the Thomsen anisotropy parameters Vp0, Vs0, ε and δ. Thomsen's γ is not typically measured with conventional VSPs as this parameter describes the behavior of horizontally polarized shear waves (SH) which are not usually generated by conventional seismic sources.